Eric Posner (Chicago Law School) and E. Glen Weyl (Chicago) have posted Voting Squared: Quadratic Voting in Democratic Politics in SSRN.
Here is the abstract:
Democratic institutions aggregate preferences poorly. The norm of one-person-one-vote with majority rule treats people fairly by giving everyone an equal chance to influence outcomes, but fails to give proportional weight to people whose interests in a social outcome are stronger than those of other people — a problem that leads to the familiar phenomenon of tyranny of the majority. Various institutions that have been tried or proposed over the years to correct this problem — including supermajority rule, weighted voting, cumulative voting, “mixed constitutions,” executive discretion, and judicially protected rights — all badly misfire in various ways, for example, by creating gridlock or corruption. This paper proposes a new form of political decision-making based on the theory of quadratic voting. It explains how quadratic voting solves the preference aggregation problem, giving proper weight to preferences of varying intensity, and how it could be implemented as well as addressing concerns about its consequences for equity.